Thermal Physics Kittel chapter 6 -- Entropy of mixing problem

[bluepilotg-2_07]

Homework Statement

Suppose that a system of N atoms of type A is placed
in diffusive contact with a system of N atoms of type B at the same temperature
and volume. Show that after diffusive equilibrium is reached the total entropy
is increased by 2N log 2. The entropy increase 2N log 2 is known as the entropy
of mixing. If the atoms are identical (A = B), show that there is no increase in
entropy when diffusive contact is established. The difference in the results has
been called the Gibbs paradox.

Relevant Equations

sigma = log(g), mu = tau*log(N/V*n_Q), sigma = N[log(V*n_Q/N)+5/2]

I've been working on this problem for the past 3 days. I have other papers with different ways of tackling the problem. However, I just cannot get to the answer (change in entropy = 2Nlog(2)).

 

[berkeman]

Welcome to PF.

Your attached picture of your work is very light and hard to read. Can you upload a better image please?

Also, I will send you a message with tips for posting math equations at PF using LaTeX. That is a much better way to show your work in the future here.